NDA 2023 Maths · Mathematics · Sets, Relations and Functions · medium

Let A⊂ B with n(A)=3 and n(B)=6. The number of sets C such that A⊆ C⊆ B is

Single correct option

Let

A\subset B

with

n(A)=3

and

n(B)=6

. The number of sets

C

such that

A\subseteq C\subseteq B

Show answer and solution

Answer: (C) 8

Every such

C

contains all 3 elements of

A

and any subset of the remaining

6-3=3

elements of

B

. Hence the count is

2^3=8

. The trap is to use

2^6=64

(all subsets of

B

) or to exclude

C=A

C=B

, which are both allowed because the inclusions are not strict.

Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake